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Teor. Veroyatnost. i Primenen., 2003, Volume 48, Issue 1, Pages 3–21 (Mi tvp298)  

This article is cited in 3 scientific papers (total in 3 papers)

Transient phenomena in a random walk

A. K. Aleshkyavichene, S. V. Nagaev

Institute of Mathematics and Informatics

Abstract: The paper studies the limit distributions of the maximum of sums $\max_{1\le k\le n}\sum_{l=1}^k\xi_{n,l}$ for the triangular array $\xi_{n,k}$, $k=1,\ldots,n$, $n=1,2,\ldots $, of independent identically distributed random variables in a singular series in cases where $a_n=E\xi_{n,k}\to 0$ and/or 1) $a_n\sqrt n\to\infty$, or 2) $a_n\sqrt n\to-\infty$, or 3) $a_n\sqrt n\to 0$ as $n\to\infty$. The direct proof that the analytic expressions for limit laws coincide was previously obtained by different authors and is given. Moreover, for these transient cases the convergence of the sequence of distributions of maximums to the limit laws is proved with the help of the characteristic functions method.

Keywords: triangular array, maximum of sequential sums, limit distributions, method of characteristic functions.

DOI: https://doi.org/10.4213/tvp298

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English version:
Theory of Probability and its Applications, 2004, 48:1, 1–18

Bibliographic databases:

Received: 17.11.1998

Citation: A. K. Aleshkyavichene, S. V. Nagaev, “Transient phenomena in a random walk”, Teor. Veroyatnost. i Primenen., 48:1 (2003), 3–21; Theory Probab. Appl., 48:1 (2004), 1–18

Citation in format AMSBIB
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\by A.~K.~Aleshkyavichene, S.~V.~Nagaev
\paper Transient phenomena in a random walk
\jour Teor. Veroyatnost. i Primenen.
\yr 2003
\vol 48
\issue 1
\pages 3--21
\mathnet{http://mi.mathnet.ru/tvp298}
\crossref{https://doi.org/10.4213/tvp298}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2013402}
\zmath{https://zbmath.org/?q=an:1056.60042}
\transl
\jour Theory Probab. Appl.
\yr 2004
\vol 48
\issue 1
\pages 1--18
\crossref{https://doi.org/10.1137/S0040585X980300}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000220694300001}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. I. Sakhanenko, “On transient phenomena in random walks”, Theory Probab. Appl., 49:2 (2005), 354–367  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Lukacs P.M., Burnham K.P., “Review of capture–recapture methods applicable to noninvasive genetic sampling”, Molecular Ecology, 14:13 (2005), 3909–3919  crossref  isi  scopus
    3. Ruell E.W., Riley S.P.D., Douglas M.R., Pollinger J.P., Crooks K.R., “Estimating bobcat population sizes and densities in a fragmented urban landscape using noninvasive capture–recapture sampling”, Journal of Mammalogy, 90:1 (2009), 129–135  crossref  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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